How can I project an object to a sphere
You can do this with a lattice and shrinkwrap modifiers.

Starting with a scene like this:

A landscape and a hemisphere



Add a lattice object, make it so it has only 1 subdivison on the W axis.
In edit mode make resize the lattice it so that it is slightly larger than the landscape. 



Place the lattice so that it lays under your landscape, not touching but the very bottom vertices of the object.



Then select the landscape, add a lattice modifier and select the lattice as deforming object.



Select the lattice object and add a shrinkwrap modifier to it. Set the hemisphere as Target. Change the Mode to Project, Direction to negative on the Z axis.